The Qatar Stars League club have paid a reported 45 million euros (£38.65 million) for the player, according to the Italian media.
"I was very proud to wear the colours of Paris Saint-Germain for more than a decade, to rub shoulders with so many great players, and to win 30 trophies," Verratti told the club website.
"Paris, the Club and its supporters will always have a very special place in my heart. I will be Parisian forever."
Verratti joined PSG in 2012 from his hometown club Pescara. The Ligue 1 side paid 12 million euros ($12.87 million) for the then 19-year-old.
In 11 seasons at PSG, Verratti played in 416 matches, making him the club's second-highest appearance-maker behind Jean-Marc Pilorget (435).
He helped PSG win nine league titles, a record in Ligue 1, along with six French Cups.
Verratti has not been part of new manager Luis Enrique's plans following the recent departures of players including Lionel Messi, Neymar and Mauro Icardi.
"Marco will forever be linked to Paris Saint-Germain," said Paris Saint-Germain President Nasser Al-Khelaifi.
"He has always been there for the Club, giving his whole heart on the pitch and achieving so many great things with us."
Verratti has won 55 international caps, scoring three goals. He was in the Italy squad that won Euro 2020, starting the final in which they beat England in a penalty shootout.
Al-Arabi finished runners-up to Al-Duhail in last season's Qatar Stars League and have started this season with three draws. The Qatari transfer window remains open until September 18th.
